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Dynamics and structure of an apolar active suspension in an annulus

Published online by Cambridge University Press:  27 November 2017

Sheng Chen ,
Peng Gao Open the ORCID record for Peng Gao [Opens in a new window]  and
Tong Gao Open the ORCID record for Tong Gao [Opens in a new window]
Sheng Chen
Affiliation:
Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824, USA
Peng Gao
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
Tong Gao*
Affiliation:
Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824, USA Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, MI 48824, USA
*
†Email address for correspondence: gaotong@egr.msu.edu
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Abstract

We study the complex dynamics of a two-dimensional suspension comprising non-motile active particles confined in an annulus. A coarse-grained liquid crystal model is employed to describe the nematic structure evolution, and is hydrodynamically coupled with the Stokes equation to solve for the induced active flows in the annulus. For dilute suspensions, coherent structures are captured by varying the particle activity and gap width, including unidirectional circulations, travelling waves and chaotic flows. For concentrated suspensions, the internal collective dynamics features motile disclination defects and flows at finite gap widths. In particular, we observe an intriguing quasi-steady-state at certain gap widths during which $+1/2$-order defects oscillate around equilibrium positions accompanying travelling-wave flows that switch circulating directions periodically. We perform linear stability analyses to reveal the underlying physical mechanisms of pattern formation during a concatenation of instabilities.

JFM classification

Complex Fluids: Complex Fluids Complex Fluids: Liquid crystals Nonlinear Dynamical Systems: Pattern formation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 835 , 25 January 2018 , pp. 393 - 405
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Copyright
© 2017 Cambridge University Press 

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References

Adams, D. W. & Errington, J. 2009 Bacterial cell division: assembly, maintenance and disassembly of the z ring. Nat. Rev. Microbiol. 7, 642–653.Google Scholar
Bingham, C. 1974 An antipodally symmetric distribution on the sphere. Ann. Stat. 2, 1201–1225.Google Scholar
Bricard, A., Caussin, J., Desreumaux, N., Dauchot, O. & Bartolo, D. 2013 Emergence of macroscopic directed motion in populations of motile colloids. Nature 503, 95–98.Google Scholar
Chaubal, C. & Leal, L. 1998 A closure approximation for liquid-crystalline polymer models based on parametric density estimation. J. Rheol. 42, 177–201.Google Scholar
Doi, M. & Edwards, S. 1988 The Theory of Polymer Dynamics, vol. 73. Oxford University Press.Google Scholar
Ezhilan, B. & Saintillan, D. 2015 Transport of a dilute active suspension in pressure-driven channel flow. J. Fluid Mech. 777, 482–522.Google Scholar
Ezhilan, B., Shelley, M. & Saintillan, D. 2013 Instabilities and nonlinear dynamics of concentrated active suspensions. Phys. Fluids 25, 070607.Google Scholar
Gao, T., Betterton, M., Jhang, A. & Shelley, M. 2017 Analytical structure, dynamics, and coarse-graining of a kinetic model of an active fluid. Phys. Rev. Fluids 2, 093302.Google Scholar
Gao, T., Blackwell, R., Glaser, M., Betterton, M. & Shelley, M. 2015a Multiscale modeling and simulation of microtubule/motor protein assemblies. Phys. Rev. E 92, 062709.Google Scholar
Gao, T., Blackwell, R., Glaser, M., Betterton, M. & Shelley, M. 2015b Multiscale polar theory of microtubule and motor-protein assemblies. Phys. Rev. Lett. 114, 048101.Google Scholar
Gao, T. & Hu, H. 2009 Deformation of elastic particles in viscous shear flow. J. Comput. Phys. 228, 2132–2151.Google Scholar
Gao, T. & Li, Z. 2017 Self-driven droplet powered by active nematics. Phys. Rev. Lett. 119, 108002.CrossRefGoogle ScholarPubMed
de Gennes, P. G. 1974 The Physics of Liquid Crystals. Oxford, Clarendon Press.Google Scholar
Giomi, L., Bowick, M., Ma, X. & Marchetti, M. 2013 Defect annihilation and proliferation in active nematics. Phys. Rev. Lett. 110, 228101.Google Scholar
Giomi, L., Mahadevan, L., Chakraborty, B. & Hagan, M. F. 2011 Excitable patterns in active nematics. Phys. Rev. Lett. 106, 218101.Google Scholar
Giomi, L., Mahadevan, L., Chakraborty, B. & Hagan, M. F. 2012 Banding, excitability and chaos in active nematic suspensions. Nonlinearity 25, 2245.Google Scholar
Guillamat, P., Ignés-Mullol, J. & Sagués, F. 2016a Control of active liquid crystals with a magnetic field. Proc. Natl Acad. Sci. USA 113 (20), 5498–5502.Google Scholar
Guillamat, P., Ignés-Mullol, J., Shankar, S., Marchetti, M. C. & Sagués, F. 2016b Probing the shear viscosity of an active nematic film. Phys. Rev.  E 94, 060602.Google Scholar
Henkin, G., Decamp, S. J., Chen, D. T. N., Sanchez, T. & Dogic, Z. 2014 Tunable dynamics of microtubule-based active isotropic gels. Phil. Trans. R. Soc. Lond. A 372 (2029), 20140142.Google Scholar
Hohenegger, C. & Shelley, M. 2011 Dynamics of Complex Bio-Fluids. Oxford University Press.Google Scholar
Hu, H., Zhu, M. & Patankar, N. 2001 Direct numerical simulations of fluid solid systems using the arbitrary Lagrangian Eulerian technique. J. Comput. Phys. 169, 427–462.Google Scholar
Jewell, E., Wang, W. & Malloukl, T. 2016 Catalytically driven assembly of trisegmented metallic nanorods and polystyrene tracer particles. Soft Matt. 12, 2501–2504.Google Scholar
Lushi, E., Wioland, H. & Goldstein, R. 2014 Fluid flows generated by swimming bacteria drive self-organization in confined fluid suspensions. Proc. Natl Acad. Sci. USA 111, 9733–9738.CrossRefGoogle Scholar
Maier, W. & Saupe, A. 1958 Eine einfache molekulare Theorie des nematischen kristallinflüssigen Zustandes. Zeit. Nat. Teil A 13, 564–566.Google Scholar
Marchetti, M., Joanny, J., Ramaswamy, S., Liverpool, T., Prost, J., Rao, M. & Simha, R. 2013 Hydrodynamics of soft active matter. Rev. Mod. Phys. 85, 1143–1189.Google Scholar
Ramaswamy, S. 2010 The mechanics and statistics of active matter. Ann. Rev. Cond. Matt. Phys. 1, 323–345.Google Scholar
Ravnik, M. & Yeomans, J. 2013 Confined active nematic flow in cylindrical capillaries. Phys. Rev. Lett. 110, 026001.Google Scholar
Saintillan, D. & Shelley, M. 2008 Instabilities, pattern formation, and mixing in active suspensions. Phys. Fluids 20, 123304.CrossRefGoogle Scholar
Saintillan, D. & Shelley, M. 2013 Active suspensions and their nonlinear models. C. R. Phys. 14, 497–517.Google Scholar
Sanchez, T., Chen, D., Decamp, S., Heymann, M. & Dogic, Z. 2012 Spontaneous motion in hierarchically assembled active matter. Nature 491, 431–434.CrossRefGoogle ScholarPubMed
Shelley, M. 2016 The dynamics of microtubule/motor-protein assemblies in biology and physics. Annu. Rev. Fluid Mech. 48, 487–506.Google Scholar
Sokolov, A., Aranson, I., Kessler, J. & Goldstein, R. 2007 Concentration dependence of the collective dynamics of swimming bacteria. Phys. Rev. Lett. 98, 158102.Google Scholar
Thampi, S., Doostmohammadi, A., Golestanian, R. & Yeomans, J. M. 2015 Intrinsic free energy in active nematics. Europhys. Lett. 112, 28004.CrossRefGoogle Scholar
Thampi, S., Golestanian, R. & Yeomans, J. 2014 Instabilities and topological defects in active nematics. Europhys. Lett. 105, 18001.Google Scholar
Theillard, M., Alonso-Matilla, R. & Saintillan, D. 2017 Geometric control of active collective motion. Soft Matt. 13, 363–375.Google Scholar
Tsang, A. C. H. & Kanso, E. 2016 Density shock waves in confined microswimmers. Phys. Rev. Lett. 116, 048101.Google Scholar
Voituriez, R., Joanny, J. & Prost, J. 2005 Spontaneous flow transition in active polar gels. Europhys. Lett. 69, 404–410.CrossRefGoogle Scholar
Wioland, H., Lushi, E. & Goldstein, R. 2016 Directed collective motion of bacteria under channel confinement. New J. Phys. 18, 075002.Google Scholar
Wioland, H., Woodhouse, F., Dunkel, J., Kessler, J. & Goldstein, R. 2013 Confinement stabilizes a bacterial suspension into a spiral vortex. Phys. Rev. Lett. 110, 268102.Google Scholar
Woodhouse, F. & Goldstein, R. 2012 Spontaneous circulation of confined active suspensions. Phys. Rev. Lett. 109, 168105.Google Scholar
Wu, K.-T., Hishamunda, J. B., Chen, D. T. N., Decamp, S. J., Chang, Y.-W., Fernández-Nieves, A., Fraden, S. & Dogic, Z. 2017 Transition from turbulent to coherent flows in confined three-dimensional active fluids. Science 355 (6331), eaal1979.Google Scholar
Wykes, M. D., Palacci, J., Adachi, T., Ristroph, L., Zhong, X., Ward, M., Zhang, J. & Shelley, M. 2016 Dynamic self-assembly of microscale rotors and swimmers. Soft Matt. 12, 4584–4589.CrossRefGoogle Scholar

Chen et al. supplementary movie 1

Supplementary movie 1: Nematic director/order (left) and flow vector/vorticity (right) for a dense Extensor suspension confined in an annulus when choosing α = -2.0, R1 = 0.75, R2 = 2.0, β = 0.874, ζ = 0.5, dT = dR = 0.025. The black scale bar represents the dimensionless length 1.0.

Download Chen et al. supplementary movie 1(Video)
Video 22.6 MB

Chen et al. supplementary movie 2

Supplementary movie 2: Nematic director/order (left) and flow vector/vorticity (right) for a dense Extensor suspension confined in an annulus when choosing α = -2.0, R1 = 0.5, R2 = 1.6, β = 0.874, ζ = 0.5, dT = dR = 0.025. The black scale bar represents the dimensionless length 1.0.

Download Chen et al. supplementary movie 2(Video)
Video 18.2 MB

Chen et al. supplementary movie 3

Supplementary movie 3: Nematic director/order (left) and flow vector/vorticity (right) for a dense Extensor suspension confined in an annulus when choosing α = -2.0, R1 = 0.75, R2 = 3.0, β = 0.874, ζ = 0.5, dT = dR = 0.025. The black scale bar represents the dimensionless length 1.0.

Download Chen et al. supplementary movie 3(Video)
Video 19.2 MB